Active Share and Mutual Fund Performance
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Financial Analysts Journal
·
Volume 69 Number 4
©2013 CFA Institute
Active Share and Mutual Fund Performance
Antti Petajisto
Using Active Share and tracking error, the author sorted all-equity mutual funds into various categories
of active management. The most active stock pickers outperformed their benchmark indices even after fees,
whereas closet indexers underperformed. These patterns held during the 2008–09 financial crisis and within
market-cap styles. Closet indexing has increased in both volatile and bear markets since 2007. Cross-sectional
dispersion in stock returns positively predicts performance by stock pickers.
S
hould a mutual fund investor pay for active In my study, following Cremers and Petajisto
fund management? Generally, the answer is (2009), I divided active managers into several cat-
no. A number of studies have concluded that egories on the basis of both Active Share, which
the average actively managed fund loses to a low- measures mostly stock selection, and tracking error,
cost index fund, net of all fees and expenses.1 which measures mostly exposure to systematic
However, active managers are not all equal: They risk. Active stock pickers take large but diversified
differ in how active they are and what type of active positions away from the index. Funds that focus
management they practice. These distinctions on factor bets generate large volatility with respect
allow us to distinguish different types of active to the index even with relatively small active posi-
managers, which turns out to matter a great deal tions. Concentrated funds combine very active
for investment performance. stock selection with exposure to systematic risk.
How should active management be measured? Closet indexers do not engage much in any type
For example, consider the Growth Fund of America, of active management. A large number of funds in
currently the largest equity mutual fund in the the middle are moderately active without a clearly
United States. The fund’s portfolio can be broken distinctive style.
down into two components: the S&P 500 Index, I started by looking at examples of different
which is the passive component, and all the devia- types of funds and then examined two famous
tions from the index, which constitute the active funds in detail. I also investigated general trends
component. If the fund is overweight in a particular in closet indexing over time and the reasons behind
stock relative to the index, it effectively has an active them. I then turned to fund performance, testing
long position in that stock; if the fund is under- the performance of each category of funds through
weight in a particular stock relative to the index, it December 2009. I separately explored fund per-
has an active short position in that stock. At the end formance in the financial crisis of January 2008–
of 2009, investing $100 in the fund was equivalent December 2009 to see whether historical patterns
to investing $100 in the S&P 500, together with $54 held up during this highly unusual period. Finally,
in the fund’s active long positions and $54 in the I tried to identify when market conditions are gen-
fund’s active short positions. The size of these active erally most favorable to active stock pickers.
positions as a fraction of the portfolio—54% in this ■■ Discussion of findings. I found that closet
case—is what I call the Active Share of the fund. indexing has been increasing in popularity since
Intuitively, it tells us the percentage of the portfolio 2007, currently accounting for about one-third of
that differs from the passive benchmark index. A all mutual fund assets. Over time, the average level
common alternative metric is tracking error, which of active management is low when volatility is
measures the time-series standard deviation of the high, particularly in the cross-section of stocks, and
return on the active positions. when recent market returns have been low, which
also explains the previous peak in closet indexing,
Antti Petajisto is a vice president at BlackRock, San in 1999–2002.
Francisco. The average actively managed fund has had
Author’s Note: This article was written when the author weak performance, losing to its benchmark by
was a finance professor at the NYU Stern School of –0.41%. The performance of closet indexers has
Business. been predictably poor: They largely just match their
July/August 2013 www.cfapubs.org 73Financial Analysts Journal
benchmark index returns before fees, and so after Types of Active Management. An active
fees, they lag behind their benchmarks by approxi- manager can add value only by deviating from his
mately the amount of their fees. Funds that focus on benchmark index in one of two ways: stock selection
factor bets have also lost money for their investors. or factor timing. Stock selection involves active bets
However, one group has added value for investors: on individual stocks—for example, selecting only
the most active stock pickers, who have beaten their one stock from a particular industry. Factor tim-
benchmarks by 1.26% a year after fees and expenses; ing, also known as tactical asset allocation, involves
before fees, their stock picks have even beaten time-varying bets on broader factor portfolios—for
the benchmarks by 2.61%, displaying a nontrivial example, overweighting particular sectors of the
amount of skill. High Active Share is most strongly economy, having a temporary preference for value
related to future returns among small-cap funds, stocks, and even choosing to keep some assets in
but its predictive power within large-cap funds is cash rather than invest in equities.
To quantify active management of mutual
also both economically and statistically significant.
funds, I followed the methodology of Cremers and
The financial crisis hit active funds severely in
Petajisto (2009). First, I used the Active Share of a
2008, leading to broad underperformance in 2008
fund, defined as
followed by a strong recovery in 2009. The general
patterns were similar to historical averages. The 1 N
Active share = ∑ w fund ,i − windex,i , (1)
active stock pickers beat their indices over the crisis 2 i =1
period by about 1%, whereas the closet indexers
where wfund,i is the weight of stock i in the fund’s
continued to underperform. portfolio, windex,i is the weight of the same stock in
Cross-sectional dispersion in stock returns the fund’s benchmark index, and the sum is com-
positively predicts benchmark-adjusted returns puted over the universe of all assets. Intuitively,
for the most active stock pickers, suggesting that Active Share is simply the percentage of the fund’s
stock-level dispersion can be used to identify mar- portfolio that differs from the fund’s benchmark
ket conditions favorable to stock pickers. Related index. For an all-equity mutual fund that has no
measures, such as the average correlation with the leveraged or short positions, the Active Share of the
market index, do not predict returns equally well. fund will always be between 0% and 100%.
My study is most closely related to Cremers Tracking-error volatility, often simply called
and Petajisto (2009); I added six more years to their tracking error, is the other measure of active manage-
sample period and extended their analysis in sev- ment that I used—specifically, the common definition
eral ways. A few other studies have also investi-
gated active management and its impact on fund (
Tracking error = stdev R fund − Rindex , ) (2)
performance, using such measures as tracking error where I computed the time-series standard devia-
relative to the S&P 500 (Wermers 2003), industry tion of the difference between the fund return, Rfund,
concentration of fund positions (Kacperczyk, Sialm, and its benchmark index return, Rindex. Intuitively,
and Zheng 2005), R2 with respect to a multifactor tracking error measures the volatility of the fund
model (Amihud and Goyenko 2010), active stock that is not explained by movements in the fund’s
selection and timing efforts inferred from daily benchmark index.
return data (Ekholm 2011), and deviations from a Conceptually, what is the difference between
passive benchmark formed on the basis of past ana- these two measures of active management? To see the
lyst recommendations (Kacperczyk and Seru 2007). difference, let us consider a portfolio with 50 stocks—
Looking at stock returns directly, Cohen, Polk, and in other words, a potentially well-diversified portfo-
Silli (2010) found that the largest active positions lio. How active management shows up in these two
of fund managers outperformed, suggesting that measures of active management depends on one key
managers should hold less diversified portfolios. question: Are the active positions exposed to sys-
Sun, Wang, and Zheng (2009) found that hedge tematic risk? For example, if all the overweight posi-
funds that deviated aggressively from their peers tions are in technology stocks, which tend to move
outperformed more conservative funds. together, even small active positions will generate a
high tracking error. Alternatively, let us assume there
are 50 industries with 20 stocks in each industry and
Measuring Active Management of
the fund picks just 1 stock out of 20 in each indus-
Mutual Funds try while keeping the same industry weights as the
In this section, I define and discuss the measures benchmark index. The fund is thus very selective
of active management that I used in my study and within industries, generating a high Active Share of
offer examples of each fund category. about 95%, but because it is not taking any positions
74 www.cfapubs.org ©2013 CFA InstituteActive Share and Mutual Fund Performance
across industries, most of the risk in its active posi- both dimensions. For example, a fund with a 4%–6%
tions will be diversified away, producing a low tracking error can have an Active Share anywhere
tracking error. from under 40% to over 90%, and a fund with an
Hence, Active Share and tracking error empha- Active Share of 60%–70% can have a tracking error
size different aspects of active management. Active anywhere from under 4% to over 14%. In other
Share is a reasonable proxy for stock selection, words, the distribution is wide enough that we can
whereas tracking error is a proxy for systematic fac- meaningfully distinguish between different active
tor risk. To get a complete picture of active manage- management styles on the basis of the two measures.
ment, we need both measures.
Figure 1 illustrates the two dimensions of active Examples of Funds. Figure 2 shows some
management and how they can be linked to differ- examples of all-equity mutual funds in each cat-
ent types of active management. Diversified stock egory, plotted along the two dimensions of active
pickers have a high Active Share and a low track- management. The numbers are from the last date
ing error, whereas funds that focus on factor bets in 2009 when the fund holdings were reported in
take the opposite approach. Concentrated funds the database (the end of September for most funds).
combine stock selection with factor bets, thus scor- The two funds plotted at the origin and mostly
ing high on both measures. Closet indexers score on top of each other are pure index funds: the
low on both measures. Later in my study, I chose Vanguard 500 Index Fund and the Fidelity Spartan
cutoffs for the categories in order to use them in the U.S. Equity Index Fund. Each fund has essentially
performance tests. zero Active Share and tracking error, as we would
Table 1 shows the actual distribution of Active expect from pure indexers. Their very low expense
Share and tracking error across all-equity funds in ratios—12 bps and 9 bps a year, respectively—
2009. Each cell contains the number of funds in that reflect their passive management approach.
group. A clear, positive correlation exists between The upper left-hand corner includes such diver-
Active Share and tracking error, but the interesting sified stock pickers as the T. Rowe Price Mid-Cap
aspect is the substantial independent variation along Value Fund, which has a high Active Share of 93%
Figure 1. Different Types of Active Management
Active Share
Diversified Concentrated
High Stock Picks Stock Picks
Closet Factor
Low Indexing Bets
Pure
Indexing
0
0 Low High
Tracking Error
Source: Cremers and Petajisto (2009).
July/August 2013 www.cfapubs.org 75Financial Analysts Journal
Table 1. Distribution of Mutual Funds across Active Share and Tracking-Error Ranges, 2009
Active Tracking Error
Share (% per year)
(%) 0–2 2–4 4–6 6–8 8–10 10–12 12–14 >14 Total
90–100 0 0 6 36 66 47 44 87 285
80–90 0 0 35 83 67 55 35 50 326
70–80 0 7 56 62 63 33 17 19 257
60–70 0 22 85 60 25 13 5 6 216
50–60 0 24 49 25 14 4 2 0 120
40–50 2 28 20 6 3 0 0 0 61
30–40 4 14 9 2 0 0 0 0 30
20–30 0 3 0 0 0 0 0 0 5
10–20 5 3 0 0 0 0 0 0 8
0–10 70 0 0 0 0 0 0 0 73
Total 82 104 262 275 238 152 103 164 1,380
Notes: This table shows the number of U.S. all-equity mutual funds in each Active Share and tracking-error category. Tracking
error is computed from daily returns over the previous six months.
Figure 2. Examples of Funds in Each Category, 2009
Active Share (%)
100
FMI Large Cap Longleaf Partners
($2 billion) Sequoia Small-Cap ($2 billion)
($3 billion)
90 T. Rowe Price
Mid-Cap Value
($7 billion)
80
70
GMO Quality
($12 billion)
AIM
Growth Fund Constellation
60
of America ($3 billion)
($140 billion)
50
40 RiverSource
Disciplined
Equity ($3 billion)
30
20
10
Vanguard 500 ($78 billion)
Fidelity Spartan ($22 billion)
0
0 5 10 15 20
Tracking Error (%)
Note: Total assets are shown in parentheses.
76 www.cfapubs.org ©2013 CFA InstituteActive Share and Mutual Fund Performance
yet a low tracking error of 5.4% relative to the S&P Data and Empirical Methodology
400 Index. This outcome is possible only if the fund’s
This section presents the data and basic empirical
sector weights are similar to those of the benchmark methodology that I used in my study.
index and the fund focuses instead on finding indi-
vidual underpriced stocks within sectors and indus- Data. To compute Active Share, I needed data
tries. Another example is the FMI Large Cap Fund, on the portfolio composition of mutual funds as
which has an Active Share of 95% and a tracking well as their benchmark indices. I matched stock
error of 5.4% with respect to the S&P 500. The fund holdings with the CRSP stock return database. I
has only 24 stock positions, but those positions are obtained data on the stock holdings of mutual funds
sufficiently well diversified across industries that its from the Thomson Reuters database, which is based
tracking error has remained low; the fund even men- on mandatory quarterly filings with the U.S. SEC.
tions its low-risk approach in its prospectus. For the funds’ benchmarks, I included essen-
Among the nonindex funds, the lower right- tially all indices used by the funds themselves
hand side includes funds that focus on factor bets, over the sample period—a total of 19 indices from
Standard & Poor’s (S&P), Russell Investments, and
which means that they have a relatively high track-
Dow Jones/Wilshire Associates, including their
ing error in spite of a moderately low Active Share.
common large-cap, mid-cap, and small-cap indices
One example is the GMO Quality Fund, with an
as well as their value and growth components. I
Active Share of only 65% but a tracking error of
obtained the index holdings data directly from the
12.9%. The fund states that it may time such factors
index providers.
as industries, sectors, size, and value and that it may
I obtained data on monthly returns for mutual
keep some assets in cash or invest in high-quality funds from the CRSP mutual fund database; these
debt instead of trying to minimize its risk relative are net returns (i.e., after fees, expenses, and bro-
to the S&P 500. In addition, the AIM Constellation kerage commissions but before any front-end or
Fund has a relatively high tracking error of 9.7% back-end loads). I obtained data on daily returns for
and a low Active Share of 66%, reflecting the sector mutual funds from multiple sources. Daily returns
bets of the fund as well as its decision to allocate to are available in the CRSP mutual fund database
cash during the financial crisis. from September 1998 on; before that period, I used
The upper right-hand corner includes con- the same combined database as in Cremers and
centrated stock pickers that combine active stock Petajisto (2009). I obtained data on both monthly
selection with factor bets. The Sequoia Fund has and daily returns for benchmark indices from
an Active Share of 97% and a tracking error of S&P, Russell Investments, and Dow Jones, and all
14.1%, which is not surprising for a fund that of those returns included dividends. All my data-
takes large positions in individual stocks. It bases were free of survivorship bias because they
holds 22 stocks in total, sometimes as few as 10, contained both live and dead funds.
and has some positions that account for 10% or
Sample Selection. Using MFLINKS, I started
more of the portfolio. Among small-cap funds,
by merging the CRSP mutual fund database with
the Longleaf Partners Small-Cap Fund has only
the Thomson Reuters holdings database. For funds
19 stocks in its portfolio, which gives it an Active
with multiple share classes, I computed the value-
Share of 99% and a tracking error of 14.4% rela-
weighted averages of all variables—including
tive to the Russell 2000 Index. monthly and daily returns, fees, and turnover—
Finally, the funds on the lower left-hand side across all share classes. To identify domestic all-
above the index funds have both a low Active equity funds, I used four different objective codes
Share and a low tracking error, indicating that from CRSP and one code from Thomson Reuters; I
they do not engage much in either stock selec- also required the average stock holdings in CRSP to
tion or factor timing. Given that such funds claim be at least 70% and the share of matched U.S. stock
to be actively managed and charge fees for active holdings to be at least 60%. I eliminated all sector
management, they can be labeled closet indexers. funds and funds below $10 million in assets. I dis-
The RiverSource Disciplined Equity Fund has an tinguished between index funds, enhanced index
Active Share of only 44% and a tracking error of funds,2 and active (nonindex) funds and flagged
3.1%. The fund holds 276 stocks, which is more each fund accordingly. To obtain reasonably accu-
than half the stocks in its benchmark index. A rate estimates of tracking error, I computed it by
new entrant in this category is the Growth Fund using data on daily returns from the six months
of America, which is wrestling with $140 billion in preceding each holdings report date. After apply-
assets and has an Active Share of only 54% and a ing these screens, I ended up with a final sample of
tracking error of 4.4%. 2,740 funds over 1980–2009.
July/August 2013 www.cfapubs.org 77Financial Analysts Journal
Differences from Cremers and Petajisto Fifth, I mapped the Thomson Reuters holdings
(2009). My methodology of identifying funds and data with the CRSP mutual fund data by using
putting the sample together followed that of Cremers MFLINKS, a product intended for that purpose.
and Petajisto (2009), with a few exceptions. First, I This approach has become standard in the aca-
preferred to use the benchmark index self-reported demic literature, but it still suffers from some omis-
by a manager in the fund prospectus whenever sions and errors, which I tried to correct manually.
possible rather than assigning the index that pro-
duced the lowest Active Share. I had two snapshots Closet Indexing: Examples and
of the “primary benchmark index” as collected by
Morningstar from fund prospectuses—one from Trends
January 2007 and the other from March 2010—and I next examined closet indexing in more detail and
I used the earlier snapshot whenever possible. If the investigated time trends in active management.
prospectus benchmark was unavailable, I picked the What Is Closet Indexing? Loosely defined,
index that produced the lowest average Active Share closet indexing is the practice of staying close to
over the previous three years. The benefit of using
the benchmark index while claiming to be an active
the prospectus benchmark is that it is the index that
manager and usually also charging management
the fund manager has publicly committed to beat,
fees similar to those of truly active managers. It is
and thus, both investor and manager focus on perfor-
hard to define exact cutoffs for the term, but Active
mance relative to that benchmark. Even if a manager
Share can serve as a useful guide for identifying
had reported a misleading benchmark, it was not an
closet indexers.
issue because I controlled for any remaining beta,
About 50% of the value of the index will always
size, value, and momentum exposures separately.
experience above-average returns and about 50%
Second, I preferred not to backdate benchmark
will always experience below-average returns rela-
index data; therefore, I used each index only after
tive to the index itself. Thus, if a manager holds
its inception date. This approach reflected the set
more than 50% of the index (i.e., has an Active
of benchmarks available to a manager at the time
Share of less than 50%), then some of the positions
of actually making the portfolio decision, rendering
the comparison more relevant. However, because cannot exist because the manager expects them
most of the indices were available by the early to outperform the index; they exist only because
1990s, this approach had essentially no impact on he wants to reduce his risk relative to the index,
performance results and only a minor impact on even when that means including negative-alpha
other results in the 1980s. stocks in the portfolio. This approach is generally
Third, I computed tracking error as the stan- the opposite of what investors pay active manag-
dard deviation of the benchmark-adjusted return ers to do. In fact, Treynor and Black (1973) showed
rather than as the residual volatility from a regres- that when investors can allocate to both an active
sion of the fund return on its benchmark index.3 fund and a passive index fund, they can achieve the
Fund performance is commonly compared with the highest possible Sharpe ratio when the active fund
benchmark index—not beta times the benchmark maximizes its information ratio (defined as alpha
index—which better captures the risk the manager per unit of tracking error).
is taking relative to the benchmark. Specifically, if Therefore, an Active Share of 50% is the theo-
the manager is timing the equity market by tem- retical minimum that a pure active manager could
porarily holding a large amount of cash, this action have—anything below that is essentially a combi-
represents meaningful risk that is captured in the nation of an active fund and an index fund.4 As
traditional tracking-error measure but not in the in Cremers and Petajisto (2009), I generally set the
regression residual. closet indexer cutoff at an Active Share of 60%,
Fourth, I added six more years to the sample, which implies that an active manager should be
extending it from December 2003 to December able to select her investments from what she con-
2009. During that time, the CRSP mutual fund data- siders the top 40% of all stocks on the basis of their
base switched its data provider from Morningstar future alphas. Alternatively, it means that an active
to Lipper. Both CRSP versions are free of survivor- manager should never fish within what she consid-
ship bias and are supposed to include all live and ers the bottom 60% of stocks because, by definition,
dead funds, but each version still lacks some of the even the best stocks in this category can just match
funds the other one has. Hence, my fund samples or barely beat the index. Note that these cutoffs are
were slightly different, and even with an identical independent of the manager’s actual beliefs: Two
methodology, I would have been unable to per- managers can come to very different conclusions
fectly match their results for the earlier period. about which stocks are likely to outperform, but
78 www.cfapubs.org ©2013 CFA InstituteActive Share and Mutual Fund Performance
each manager should still actively invest on the and the issue remained unresolved.5 Nevertheless,
basis of his own beliefs. one can shed some light on the issue by computing
The problem with closet indexing is not that a Fidelity Magellan’s Active Share, which is shown
low Active Share is inherently bad; in fact, a ratio- in Figure 3 over 1980–2009. Fidelity Magellan did
nal investor could well combine a position in a very indeed start out as a very active fund under Peter
active fund with a position in an index fund, thus Lynch, with an Active Share over 90%. Its Active
ending up with a low Active Share in his overall Share declined toward the end of Lynch’s tenure
portfolio. The problem is that closet indexers are but then came back up again to almost 80% under
very expensive relative to what they offer. A closet Jeffrey Vinik. After Stansky took over in June 1996,
indexer charges active management fees on all the however, Active Share plunged more than 30 per-
assets in the mutual fund, even when some of the centage points (pps) to 40% in just two years, and it
assets are simply invested in the benchmark index. then kept going down until stabilizing at 33%–35%
If a fund has an Active Share of 33%, then fund- for the rest of his tenure. This remarkable shift in
level annual expenses of 1.5% amount to 4.5% of the fund’s policy represents a conscious decision to
the active positions of the fund. Because only the become a closet indexer.
active positions of the fund can possibly outper- Not surprisingly, performance suffered dur-
form the benchmark, it is very difficult in the long ing the closet indexing period. The fund lagged
run for a closet indexer to overcome such fees and behind the S&P 500 by about 1% a year for 10 years.
beat its index net of all expenses. Although not a disastrous performance, it is exactly
what you would expect from a closet indexer:
Fidelity Magellan. Fidelity Magellan is still essentially the same return as the benchmark index,
famous for its spectacular record under Peter Lynch minus about 1% in fees and expenses for suppos-
from 1977 to 1990. In his last 10 years as fund man- edly active management.
ager, Lynch beat the S&P 500 by a stunning 150%. Under pressure to make the fund more active
Riding on this track record, the fund attracted large again, Fidelity appointed Harry Lange to replace
inflows and later became the largest mutual fund Stansky on 31 October 2005. Lange was well
in the United States, with more than $100 billion in known as a bold and active manager, and thus
assets in 2000. The fund’s subsequent performance, his appointment was intended to dispel any sus-
however, has been mixed. During Robert Stansky’s picions about closet indexing, which the fund’s
tenure as fund manager from 1996 to 2005, perfor- Active Share confirms: In the three months from
mance was weak and the formerly active fund was September to December 2005, its Active Share
suspected of being a closet indexer. Such claims jumped from less than 40% to 66%. It has subse-
were vehemently denied by the fund manager, quently increased to as high as 80%, comfortably
Figure 3. Fidelity Magellan’s Active Share, 1980–2009
Active Share (%)
100
90
80
70
60
50
40
30
20
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09
Peter Lynch Morris J. Smith Jeffrey N. Vinik
Robert E. Stansky Harry Lange
Note: Active Share is shown for each fund manager at year-end.
July/August 2013 www.cfapubs.org 79Financial Analysts Journal
away from closet indexing. The fund’s perfor- The inflows have followed good performance.
mance has also become more detached from the Interestingly, the fund underperformed the S&P 500
benchmark index; as of June 2008, Lange was 6% over 1980–1998 by almost 0.5% a year, but it beat the
ahead of the index after fees, but he suffered heavy index by a remarkable 56% over September 1998–
losses in the fall of 2008. February 2000. From February 2000 to December
Even though large funds generally tend to be 2009, its performance was much steadier but still
less active than small funds, asset growth does not more than 1% a year after fees. However, its recent
explain the patterns in Fidelity Magellan’s Active fall in Active Share suggests that this good perfor-
Share. Its assets grew from $20 billion to $55 bil- mance will be hard to maintain.
lion under Vinik, yet he simultaneously increased Nevertheless, one possibly redeeming feature of
the fund’s Active Share from 62% to 76%. Under the fund is its unusual organizational structure. Its
Stansky, the fund’s assets did keep growing but only assets are divided among 10 autonomous portfolio
after he had significantly tilted toward the index. managers, whereby each manager has full responsi-
bility for his own subportfolio. Thus, if the fund is
Growth Fund of America. Currently by far
effectively a portfolio of 10 individual mutual funds,
the largest equity mutual fund in the United States,
it is possible that individual managers are very active,
the Growth Fund of America had more than $140
even if some of their bets cancel out when aggregated
billion in assets at the end of 2009. In spite of its
into the bigger fund. Still, investors should be cau-
popularity, it has both a low Active Share and a low
tious because for any regularly structured mutual
tracking error, placing it solidly in the closet indexer
fund, a drop in Active Share to closet indexing terri-
category. Can the fund really be a closet indexer?
tory would be a signal that its best days are behind it.
Figure 4 shows the fund’s Active Share and
total assets over 1981–2009. Although the fund has Trends in Closet Indexing. Are there any gen-
generally been active, its Active Share has been eral trends in closet indexing? Figure 5 shows the
declining over time, falling to only 54% at the end fraction of U.S. mutual fund assets in five Active
of 2009. Simultaneously, the fund’s assets have Share categories over 1980–2009. The bottom group
grown from under $40 billion in 2002 to as much as of funds, with Active Share below 20%, consists of
$200 billion in 2007. pure index funds, which grew from almost nothing
Figure 4. Growth Fund of America’s Active Share and Assets, 1981–2009
Active Share (%) Total Net Assets ($ billions)
100 200
180
Active Share
90
160
140
80
120
70 100
80
60
60
40
50
Assets 20
40 0
81 83 85 87 89 91 93 95 97 99 01 03 05 07 09
Note: Active Share and total net assets are shown at year-end.
80 www.cfapubs.org ©2013 CFA InstituteActive Share and Mutual Fund Performance
Figure 5. Evolution of Active Share, 1980–2009
Share of Mutual Fund Assets (%)
100
90
80
70
60
50
40
30
20
10
0
81 83 85 87 89 91 93 95 97 99 01 03 05 07 09
80%–100% 60%–80% 40%–60% 20%–40% 0%–20%
Notes: This figure shows the fraction of assets in U.S. all-equity mutual funds in each Active Share
category. The bottom category, with Active Share below 20%, contains pure index funds; the next two
categories contain the closet indexers.
in 1980 to one-fifth of mutual fund assets at the end the article) shows up as an even more significant
of 2009. The next two groups of funds, with Active predictor. This outcome can arise in response to
Share between 20% and 60%, are the closet index- tracking-error targets: When cross-sectional volatil-
ers. It appears that closet indexing has become ity increases, tracking error will increase unless a
even more popular than pure indexing, with the manager reduces the size of her active positions.
closet indexers accounting for about one-third of Recent market returns also play a role. The trail-
all mutual fund assets at the end of 2009. ing three-year average benchmark index return is
To understand the trends in closet indexing, I positively related to average Active Share, confirm-
investigated how the average level of Active Share ing that managers collectively tend to be more active
across all funds can be explained with other variables. when their investors are sitting on capital gains.
I focused on two potential explanations: market vola- However, this relationship is insignificant for the aver-
tility and recent fund returns. High market volatility age benchmark-adjusted performance of managers.
amplifies any return differences between the port- Closet indexing peaked in 1999–2002, declined
folio and the benchmark index, and underperform- until 2006, and then increased again from late 2007
ing the benchmark may be particularly painful in a to 2009 toward its prior peak. Consistent with these
down market, where everyone is suffering losses, as patterns, the VIX was high at about 25% through-
opposed to an up market, where investors are making out 1998–2002, cross-sectional volatility was also
money even when they are trailing the benchmark. high, and the market fell dramatically in 2000–2002.
Table 2 shows the monthly time-series regres- Closet indexing declined in 2003, when the market
sion results. The trailing one-year moving aver- recovered strongly and volatility came down, and
age of the CBOE Volatility Index (VIX) negatively it kept going down until 2006. In 2007, volatility
predicts average Active Share. However, the trail- shot back up when the subprime crisis started and
ing one-year average of cross-sectional dispersion substantial economic uncertainty appeared, fol-
in stock returns (discussed in more detail later in lowed by even more extreme market volatility and
July/August 2013 www.cfapubs.org 81Financial Analysts Journal
Table 2. Explaining Average Active Share, January 1990–December 2009
(t-statistics in parentheses)
(1) (2) (3) (4) (5) (6)
VIX –0.2462** 0.0973
(–2.30) (0.88)
CrossVol –0.8749*** –1.0127*** –0.8044***
(–3.78) (–5.34) (–3.23)
Index return 0.0409*** 0.0468** 0.0345***
(2.85) (2.43) (3.05)
Active return –0.2211 0.0895
(–1.53) (0.69)
N 239 239 239 239 239 239
R2 25.2% 38.7% 21.8% 11.4% 55.1% 53.9%
Notes: The dependent variable is the monthly equal-weighted average Active Share across U.S. all-equity mutual funds. VIX
is the volatility index, and CrossVol is the monthly cross-sectional dispersion for all U.S. equities; both are computed as
12-month trailing averages. Index return is the average return on the benchmark indices across all funds, and active return is
the average fund net return relative to the benchmark; both are computed as 36-month trailing averages. The t-statistics are
based on Newey–West standard errors with 36 monthly lags. Index funds, sector funds, and funds with less than $10 million
in assets were excluded.
**Significant at the 5% level.
***Significant at the 1% level.
declines in 2008. Simultaneously, closet indexing Categories of Funds. Funds can be sorted into a
reared its head again, climbing all the way back to 5 × 5 grid of Active Share and tracking error to distin-
its previous peak by 2009. guish between different types and degrees of active
One initial trigger for closet indexing might management. Because I wanted to simplify this 5 ×
also be the SEC’s decision in 1998 to require all 5 grid and make it economically more meaningful, I
mutual funds to disclose a benchmark index in created categories of funds on the basis of the grid and
their prospectuses. Presumably, this requirement labeled them according to the broad type of active
made both investors and managers more aware of management they engaged in. I included only active
benchmarks, which is desirable in itself but may (nonindex) funds in the grid; both index funds and
also have increased managers’ incentives to mini- enhanced index funds were eliminated at this stage.
mize risk relative to the benchmark. I sorted funds sequentially, first by Active Share and
then by tracking error, within each quintile.
Results on Fund Performance Table 3 shows how I formed the groups. I labeled
Investigating the type and degree of active manage- the lowest–Active Share quintile “closet indexers,”
ment can help us understand the inputs of a fund’s reflecting their mean Active Share of less than 60%.
portfolio. But how do these inputs translate into The exception is the funds with the highest tracking
outputs—or, more specifically, fund performance— error. These funds generate significant volatility rela-
across the different types of actively managed funds tive to their very small active positions, and because
and over a long period? those positions must be exposed to systematic factor
Table 3. Different Types of Active Management
Tracking-Error Quintile
Active Share 1 5
Quintile (Low) 2 3 4 (High) Group Label
5 (high) 5 5 5 5 4 5 Stock pickers
4 2 2 2 2 3 4 Concentrated
3 2 2 2 2 3 3 Factor bets
2 2 2 2 2 3 2 Moderately active
1 (low) 1 1 1 1 3 1 Closet indexers
Notes: This table shows the cutoffs I used to define different types of active management for U.S. all-equity mutual funds. I
sorted all funds into quintiles, first by Active Share and then by tracking error, using the latest values available for each fund
at the end of each month. Index funds, sector funds, and funds with less than $10 million in assets were excluded.
82 www.cfapubs.org ©2013 CFA InstituteActive Share and Mutual Fund Performance
risk, I labeled them “factor bets.” In fact, all groups funds generating the greatest turnover. With respect
in the highest-tracking-error quintile can be labeled to turnover and fees, closet indexers appear slightly
factor bets because they are all exposed to systematic less expensive than other actively managed funds,
risk in their active positions. The only exception is but they are, of course, still substantially more expen-
the highest–Active Share group. These funds com- sive per unit of Active Share or tracking error.
bine high volatility with a high degree of stock selec-
Overall Performance Results. How does fund
tion and thus fall into the “concentrated” group.
Nonconcentrated funds with high Active Share form performance vary across the different categories
the group of more diversified “stock pickers.” The of actively managed funds? I looked at both “net
rest of the funds can be called “moderately active” returns,” which I defined as investors’ returns after
because they fall in the middle in terms of both all fees and transaction costs, and “gross returns,”
Active Share and tracking error. For purposes of my which I defined as the hypothetical returns on the dis-
study, I focused on the performance results for these closed portfolio holdings. Gross returns help identify
five groups rather than using the more complicated whether any categories of funds have skill in select-
matrix of 25 portfolios. ing portfolios that outperform their benchmarks,
Table 4 shows some sample statistics for the and net returns help determine whether any such
fund groups. For each month, I computed the mean skill survives the fees and transaction costs of those
and standard deviation of a variable and then com- funds. My sample period for the performance results
puted the time-series averages across all the months. was January 1990–December 2009, thus excluding
A typical month has a total of 1,124 funds, with about the 1980s, when almost all funds were very active.
180 funds each in the stock picker, factor bet, and Table 5 shows the equal-weighted returns for
closet indexer groups. Average fees are 1.27% and the five groups of funds, as well as the averages
are comparable across all groups, although concen- across all groups. Looking at gross returns across all
trated funds are slightly more expensive and closet fund groups, I found that the average fund was able
indexers slightly cheaper. The average fund holds to select a portfolio of stocks that beat its benchmark
104 stock positions, with closet indexers holding an index by 0.96% a year before fees and expenses.
average of 161. Stock pickers hold only 66 stocks, When I used the four-factor model of Carhart (1997)
which is almost as few as the 59 stocks held by con- to control for any remaining exposure to market,
centrated funds, showing that these two groups do size, value, or momentum, that outperformance fell
indeed differ from each other, mostly because of to 0.31%. Most of the outperformance came from
their systematic risk exposure and not because of a the stock pickers and concentrated funds, with
different number of positions. The average portfolio benchmark-adjusted returns of 2.61% and 1.64%,
turnover is 87%, with factor bets and concentrated respectively. Moderately active funds also exhibited
Table 4. Sample Statistics for Fund Categories, 1990–2009
No. of Assets Active Tracking Expense No. of
Group Label Funds (millions) Share Error Turnover Ratio Stocks
A. Mean values
5 Stock pickers 180 $430 97% 8.5% 83% 1.41% 66
4 Concentrated 45 463 98 15.8 122 1.60 59
3 Factor bets 179 1,412 79 10.4 104 1.34 107
2 Moderately active 541 902 83 5.9 84 1.25 100
1 Closet indexers 180 2,009 59 3.5 69 1.05 161
All 1,124 $1,067 81% 7.1% 87% 1.27% 104
B. Standard deviations
5 Stock pickers $858 1.4% 1.9% 78% 0.40% 40
4 Concentrated 1,164 1.5 4.3 132 0.66 48
3 Factor bets 5,174 12.2 4.2 106 0.49 137
2 Moderately active 2,575 7.5 1.5 74 0.40 98
1 Closet indexers 6,003 9.3 0.9 54 0.39 177
All $3,846 14.0% 3.7% 83% 0.45% 119
Notes: This table shows sample statistics for the fund categories defined in Table 3 and subsequently used in the performance
tables. The equal-weighted mean and standard deviation of each variable are first computed for each month over the sample
period, and the reported numbers are their time-series averages across all the months.
July/August 2013 www.cfapubs.org 83Financial Analysts Journal
Table 5. Fund Performance, January 1990–December 2009
(t-statistics in parentheses)
Gross Return Net Return
Benchmark Four-Factor Benchmark Four-Factor
Group Label Adjusted Alpha Adjusted Alpha
5 Stock pickers 2.61 2.10 1.26 1.39
(3.42) (2.72) (1.95) (2.10)
4 Concentrated 1.64 0.52 –0.25 –0.89
(0.90) (0.40) (–0.17) (–0.72)
3 Factor bets 0.06 –1.02 –1.28 –2.19
(0.06) (–1.47) (–1.31) (–3.01)
2 Moderately active 0.82 0.20 –0.52 –0.78
(1.63) (0.39) (–1.16) (–1.81)
1 Closet indexers 0.44 0.13 –0.91 –1.07
(1.67) (0.51) (–3.38) (–4.46)
All 0.96 0.31 –0.41 –0.71
(1.70) (0.61) (–0.86) (–1.59)
5–1 Difference 2.17 1.96 2.17 2.45
(3.31) (3.04) (3.48) (4.00)
Notes: This table shows the annualized equal-weighted performance of U.S. all-equity mutual funds for five
types of active management (defined in Table 3). Gross returns are returns on a fund’s stock holdings and do not
include any fees or transaction costs. Net returns are returns to a fund investor after fees and transaction costs.
The numbers are expressed in percent per year, followed by t-statistics based on White’s standard errors. Index
funds, sector funds, and funds with less than $10 million in assets were excluded.
slight skill, but funds taking factor bets did not. Not (2009) found very similar results for their shorter
surprisingly, closet indexers largely just matched period, except for one group: concentrated funds.
their benchmark indices before fees and expenses. That group suffered over 2004–2009 and especially
The difference in the performance of stock picks during the financial crisis, which explains part of the
between closet indexers and stock pickers is 2.17% difference in the results.6
(t = 3.31), which is statistically significant. An alternative approach would be to use the
Looking at net returns after fees and transac- same 5 × 5 grid as in Table 3 but, instead of form-
tion costs, I found that the average fund underper- ing quintiles on the basis of absolute levels of Active
formed its benchmark by about –0.41%. Moderately Share and tracking error, form quintiles on the basis
active funds experienced a slight underperfor- of a fund’s ranking relative to funds within its own
mance of –0.52%. Factor bets turned out very poorly style group. Thus, I also formed the 5 × 5 grid sepa-
for investors, generating a –1.28% benchmark- rately for large-cap, mid-cap, and small-cap funds
adjusted return. Closet indexers predictably lost and then formed the fund groups within each of
to their indices by –0.91%, which was only slightly the three styles. The results from this analysis (unre-
less than their fees. Even concentrated funds essen- ported) are broadly similar to the earlier results:
tially just matched their benchmarks net of fees. Before fees, the best performance is exhibited by stock
The only group that added value for investors was pickers and concentrated funds, which beat their
active stock pickers; they beat their benchmarks by indices by 2.54% and 0.98%, respectively. After fees,
1.26%, or by 1.39% for the four-factor model. The only stock pickers beat their benchmarks, by 0.89%
stock pickers also beat the closet indexers net of a year. The performance improvement over closet
fees by a statistically significant 2.17% (t = 3.48). indexers is still economically and statistically signifi-
Economically, these results mean that stock selec- cant; however, because closet indexing is more com-
tion as indicated by high Active Share is rewarded mon in large-cap funds than in small-cap funds, this
in the stock market, and the most aggressive stock methodology will mitigate the difference between
pickers are able to add value for their investors even the two active management types. Even if funds are
net of all expenses. In contrast, factor bets, as indi- divided into nine styles (as in the 3 × 3 Morningstar
cated by high tracking error, are not rewarded in Style Box) on the basis of both market-cap and value
the market; on average, those funds have destroyed dimensions before being sorted into the five active
value for their investors. Cremers and Petajisto management types, the results remain similar.
84 www.cfapubs.org ©2013 CFA InstituteActive Share and Mutual Fund Performance
Fund Size and Performance. All performance the subsequent annualized returns on these port-
numbers throughout this article are equal-weighted folios net of all expenses.
averages across funds so that individual fund cat- The benchmark-adjusted returns in Panel A
egories would not be dominated by one or two exhibit considerable persistence for the concentrated
very large funds. However, Table 6 shows how funds. Prior-year winners beat prior-year losers by
fund size affects performance net of all expenses 10.04% in the following year, with the spread arising
within each of the five categories. The relationship equally from both winners and losers. Stock pickers,
between size and performance is very weak. The factor bets, and moderately active funds also display
some performance persistence, with the prior-year
best performers are the smallest funds within the
winners beating prior-year losers by about 3% in
stock picker group, earning 1.84% a year net of fees,
the following year. However, statistical significance
but this relationship is not even monotonic for any
for concentrated funds (t = 2.28) is not meaningfully
of the groups. From prior literature, we know that higher than for the other groups because it is also the
fund size in general hurts performance (see, e.g., smallest group. Only closet indexers do not exhibit
Chen, Hong, Huang, and Kubik 2004). However, much persistence: All five prior-return quintiles have
this effect arises not within but, rather, across the about equally poor performance going forward.
groups. Closet indexers tend to be larger and to per- Panel B shows the results when controlling
form poorly, whereas the most active stock pickers for the momentum factor of Carhart (1997). As
tend to be smaller funds. In other words, fund size in the prior literature, this approach eliminates a
seems to hurt performance because it is correlated large amount of performance persistence across
with the type of active management, not because it funds and indicates that the top-performing funds
hurts performance within a type. buy stocks with positive momentum. In fact, Lou
(2010) suggested that the funds themselves may
Performance Persistence. If some fund even push the value of their current holdings up
managers have skill but others do not, we would because of the new inflows they receive and invest
expect to see persistence in fund performance. in their existing positions. However, concentrated
To examine this notion, I sorted funds within funds exhibit economically significant performance
each group into quintiles on the basis of their persistence even after controlling for stock-level
benchmark-adjusted net returns over the prior momentum, with the prior winners beating the prior
calendar year (see Carhart 1997). Table 7 shows losers by 4.61% a year. In contrast, among the more
Table 6. Fund Size and Performance, January 1990–December 2009
(t-statistics in parentheses)
Fund Size Quintile
1 5
Group Label (Low) 2 3 4 (High) All High – Low
5 Stock pickers 1.84 0.89 1.05 1.16 1.38 1.26 –0.46
(2.44) (1.22) (1.42) (1.56) (1.73) (1.95) (–0.69)
4 Concentrated –1.99 0.13 0.81 0.17 –0.63 –0.25 1.36
(–1.11) (0.07) (0.49) (0.08) (–0.32) (–0.17) (0.73)
3 Factor bets –1.73 –1.11 –1.04 –1.61 –0.97 –1.29 0.75
(–1.84) (–1.20) (–0.93) (–1.47) (–0.83) (–1.32) (1.03)
2 Moderately active –0.67 –0.52 –0.49 –0.21 –0.73 –0.52 –0.06
(–1.41) (–1.14) (–1.04) (–0.41) (–1.40) (–1.17) (–0.15)
1 Closet indexers –0.88 –1.05 –0.99 –0.85 –0.83 –0.92 0.06
(–2.98) (–3.90) (–3.26) (–3.04) (–2.19) (–3.44) (0.22)
All –0.52 –0.45 –0.35 –0.31 –0.44 –0.41 0.08
(–1.20) (–1.01) (–0.71) (–0.57) (–0.77) (–0.88) (0.24)
5–1 Difference 2.72 1.93 2.04 2.01 2.20 2.18
(3.44) (2.64) (2.92) (2.84) (2.88) (3.49)
Notes: This table shows the annualized equal-weighted performance of U.S. all-equity mutual funds for fund size quintiles
within five types of active management (defined in Table 3). Returns are net returns to a fund investor after fees and transac-
tion costs. The numbers are expressed in percent per year, followed by t-statistics based on White’s standard errors. Index
funds, sector funds, and funds with less than $10 million in assets were excluded.
July/August 2013 www.cfapubs.org 85Financial Analysts Journal
Table 7. Performance Persistence, January 1990–December 2009
(t-statistics in parentheses)
Prior One-Year Return Quintile
1 5
Group Label (Low) 2 3 4 (High) All High – Low
A. Benchmark-adjusted net return
5 Stock pickers –0.26 0.78 1.22 1.39 2.93 1.22 3.20
(–0.20) (0.85) (1.68) (1.82) (2.72) (1.88) (1.68)
4 Concentrated –5.34 –2.42 –1.07 1.87 4.70 –0.41 10.04
(–2.15) (–1.24) (–0.63) (0.94) (1.56) (–0.27) (2.28)
3 Factor bets –2.74 –2.30 –1.88 –0.90 0.88 –1.38 3.62
(–1.96) (–2.61) (–1.69) (–0.63) (0.45) (–1.43) (1.34)
2 Moderately active –1.65 –1.17 –0.81 –0.20 1.30 –0.51 2.95
(–2.09) (–2.20) (–1.78) (–0.38) (1.50) (–1.12) (2.22)
1 Closet indexers –1.25 –1.11 –0.97 –0.84 –0.36 –0.91 0.89
(–3.10) (–3.69) (–3.48) (–2.55) (–0.71) (–3.32) (1.31)
All –1.66 –1.06 –0.68 –0.07 1.35 –0.42 3.02
(–2.00) (–1.95) (–1.47) (–0.11) (1.35) (–0.90) (1.97)
5–1 Difference 0.99 1.89 2.19 2.23 3.30 2.13
(0.90) (2.20) (3.08) (3.14) (3.79) (3.38)
B. Four-factor alpha of benchmark-adjusted net return
5 Stock pickers 0.87 1.50 1.39 1.01 1.87 1.34 1.00
(0.78) (1.83) (1.81) (1.29) (2.06) (2.00) (0.70)
4 Concentrated –3.38 –1.82 –1.49 0.48 1.24 –0.96 4.61
(–1.72) (–0.96) (–0.90) (0.30) (0.61) (–0.76) (1.54)
3 Factor bets –2.02 –2.18 –3.08 –2.62 –1.73 –2.32 0.29
(–1.62) (–2.65) (–3.74) (–2.86) (–1.46) (–3.18) (0.16)
2 Moderately active –1.24 –1.14 –0.90 –0.77 0.12 –0.79 1.35
(–1.69) (–2.12) (–2.13) (–1.65) (0.19) (–1.80) (1.38)
1 Closet indexers –1.07 –1.04 –1.08 –1.09 –1.06 –1.07 0.01
(–2.74) (–3.60) (–4.21) (–4.09) (–2.97) (–4.44) (0.01)
All –1.07 –0.88 –0.92 –0.77 –0.04 –0.74 1.03
(–1.43) (–1.61) (–2.08) (–1.57) (–0.06) (–1.63) (1.00)
5–1 Difference 1.94 2.55 2.47 2.11 2.93 2.41
(1.97) (3.42) (3.41) (2.78) (3.51) (3.87)
Notes: This table shows the annualized equal-weighted performance of U.S. all-equity mutual funds for prior one-year return
quintiles within five types of active management (defined in Table 3). Returns are net returns to a fund investor after fees and
transaction costs. The numbers are expressed in percent per year, followed by t-statistics based on White’s standard errors.
Index funds, sector funds, and funds with less than $10 million in assets were excluded.
diversified stock pickers, the prior winners beat the expenses, and price impact. But the persistence
prior losers by only 1.00%. The finding by Cremers results do not necessarily tell us anything about
and Petajisto (2009) of considerable performance the average level of skill between the two groups;
persistence within the highest–Active Share quintile instead, they suggest that the dispersion of skill
thus appears to have been mostly due to the concen- within each of the two groups is different. If the
trated rather than the diversified stock pickers. concentrated funds have both extremely good and
Why do the concentrated funds exhibit so extremely bad managers whereas the stock pickers
much more performance persistence than the stock are generally good managers but do not have much
pickers? Fund manager performance and skill are, heterogeneity, then the persistence results should
of course, closely related. Skill can even be defined look the way they do. For example, some small
as expected (ex ante) performance before fees, and unskilled fund managers might be tempted
86 www.cfapubs.org ©2013 CFA InstituteActive Share and Mutual Fund Performance
to take very large random bets in an attempt to lower tracking error, and so it does not offer similar
“win the lottery,” become a top-performing fund, gambling incentives for unskilled managers.
and attract large inflows (somewhat similar to the
tournament behavior in Brown, Harlow, and Starks Multivariate Evidence on Performance. Could
1996), which would place them in the same fund it be that fund categories as well as Active Share proxy
group as genuinely talented managers who take for other known variables that, in turn, predict fund
large high-conviction bets on companies they have returns? Table 8 addresses this question by show-
thoroughly researched and strongly believe are ing the results of pooled panel regressions in which
undervalued. The stock picker category has a much I tried to explain fund performance net of expenses
Table 8. Predictive Regressions for Fund Performance, 1992–2009
(t-statistics in parentheses)
Benchmark-Adjusted Return Four-Factor Alpha
(1) (2) (3) (4) (5) (6)
Active Share 0.0739*** 0.0609**
(2.76) (2.24)
Active Share × Large-cap 0.0867** 0.0492**
(2.09) (2.01)
Active Share × Mid-cap 0.1023* 0.1288**
(1.84) (2.47)
Active Share × Small-cap 0.1635** 0.1446*
(2.03) (1.90)
Stock pickers 0.0288** 0.0211**
(2.48) (2.06)
Concentrated 0.0014 0.0071
(0.07) (0.59)
Factor bets –0.0010 –0.0035
(–0.12) (–0.68)
Moderately active 0.0090** 0.0041*
(2.10) (1.69)
Tracking error –0.0827 –0.1019 –0.0855 –0.0859
(–0.54) (–0.69) (–0.85) (–0.86)
Turnover 0.0019 0.0030 0.0030 –0.0026 –0.0018 –0.0019
(0.32) (0.51) (0.48) (–0.85) (–0.58) (–0.61)
Expenses –1.3423*** –1.3281*** –1.1162** –1.3978*** –1.4187*** –1.2686***
(–3.31) (–3.45) (–2.41) (–7.64) (–7.88) (–6.25)
log10(TNA) –0.0040 0.0011 –0.0024 –0.0001 0.0032 0.0021
(–0.36) (0.10) (–0.22) (–0.01) (0.40) (0.26)
Fund age/100 –0.0153** –0.0170** –0.0163** –0.0154** –0.0148** –0.0165**
(–2.16) (–2.43) (–2.33) (–2.05) (–2.15) (–2.29)
Control variables Yes Yes Yes Yes Yes Yes
N 11,534 11,534 11,534 11,534 11,534 11,534
R2 11.0% 11.3% 11.0% 7.8% 8.1% 7.7%
Notes: The dependent variable in columns 1–3 is the cumulative net return (after all expenses) in excess of the benchmark
index return in year t; the independent variables are measured at the end of year t – 1. The dependent variable in columns
4–6 is the four-factor alpha of the benchmark-adjusted return. Large-cap, mid-cap, and small-cap are dummy variables
interacted with Active Share. Columns 3 and 6 include dummy variables for fund categories. Control variables include
returns and flows over the previous one to three years, fund size squared, number of stocks, and manager tenure. All
specifications include year dummies. Log10(TNA) is the base-10 logarithm of total net assets. The t-statistics are based on
standard errors clustered by year.
*Significant at the 10% level.
**Significant at the 5% level.
***Significant at the 1% level.
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